The present study is relevant to solve second order nonlinear second order two-point boundary value problems by using fast, rapid and efficient numerical schemes named as Adams numerical scheme and implicit Runge-Kutta scheme. These numerical schemes are implemented straightforward. Fourdifferent examples based on second order nonlinear second order two-point boundary value problems have been solved and their numerical results have been compare with the exact solution that show the correctness and exactness of the both numerical Adams nscheme and implicit Runge-Kutta schemes. The details of the achieved numerical results in the form of tables as well as figures have been discussed